A Lyapunov Krasovskii method for the stability of the Foschini-Miljanic algorithm under time-varying delays: An Independent of Delays approach

Many of the distributed power control algorithms for wireless networks in the literature ignore the fact that while the algorithms necessitate communication among users, time-delays do exist in the network. This problem is of vital importance, since time-delays are omnipresent in wireless networks. The Foschini-Miljanic (FM) algorithm is provably stable if there are no time-delays in the execution of the algorithm or when these delays are constant. This work presents a more realistic version of the well known Foschini-Miljanic algorithm for Distributed Power Control since it considers the robustness of the algorithm in the presence of time-varying delays. Using the classical Lyapunov-Krasovskii functional we prove that the FM algorithm is Globally Asymptotically Stable (GAS) for arbitrarily large time-varying delays, given the delay derivative is less than one. The validity of our results are shown through illustrative examples.